# Accounting for the Spatio-Temporal Variability of Pollutant Processes in Stormwater TSS Modeling Based on Stochastic Approaches

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hydrological Model URBS

#### Model Implementation

#### 2.2. Stormwater Quality Modeling

#### 2.2.1. Stochastic Approach

#### 2.2.2. The Models

_{1}and C

_{2}(Equation (1)). After the selection of the values of the EMC and the parameters, the initial available mass at the beginning of the rainfall event is calculated using the following Equation (2):

^{2}) during the time step dt; $Q\left(t\right)$ is the runoff rate at time t expressed as water depth per time step (mm/h); ${M}_{build-up}\left(t\right)$ is the available mass for erosion (g/m

^{2}) at time t; ${C}_{1}$ and ${C}_{2}$ are the wash-off parameters; ${M}_{build-up}\left(initial\right)$ is the available mass at the beginning of the rainfall event (mg); $EMC$ is the event mean concentration (mg/L); ${V}_{total}$ is the total runoff volume for the corresponding rainfall event (liter); $Q\left({t}_{1}\right)$ is the runoff rate at the first time step of the rainfall event (mm/h); dt is the time step (minutes); and N is the total time step of the event.

^{2}); $EMC$ is the event mean concentration (mg/L); ${V}_{total}$ is the total runoff volume for the corresponding rainfall event (L); $Q\left(i\right)$ is the instantaneous flow at time i (L/s); dt is the time step; and N is the total time step of the event.

#### 2.2.3. Boundaries of the Sampling Ranges

_{1}and C

_{2}correspond to the lowest and highest values obtained from the best cases investigated in an earlier study conducted within the same catchment [11]. As for the M(V) curve coefficient b, the boundaries are selected to replicate first flush and uniformly distributed events, since the occurrence of last flush events within the region was rare during the monitored period. The sampling ranges for the wash-off parameters are identical for all land uses, while the EMC is distinguished for each land use. With the exception of the EMC for roofs, the sampling ranges for the wash-off parameters and the EMC for roads are determined by prior knowledge acquired on the site. This method faces difficulties in setting appropriate values for sampling ranges.

#### 2.3. Catchment and Data Description

^{2}> 0.98:

#### 2.4. Evaluation Criterion of the Model Performance

#### 2.5. Model Application

## 3. Results and Discussion

#### 3.1. Water Flow Simulations

_{Nash}and C

_{R}

_{²}≥ 0.9.

_{Nash}and C

_{R}

_{²}were higher than 0.7. Visual inspection of the simulated and observed hydrographs showed that the model provided a good replication of the overall trend in runoff generation (Figure 4). A minor time offset is observed for the second event on 8 October and the event on 13 December. The measured peak flows are slightly ahead of simulated peaks, possibly due to the simple routing scheme used to describe the transfer function. Using more robust numerical schemes based on Barre de St Venant equations might give a better performance. However, this effect is minimal in all cases and does not occur in all events.

_{Nash}for both runoff volumes and instantaneous flow are slightly lower than those calculated for the calibration period with values equal to 0.57 and 0.58, respectively. This is attributed to the parameters, which may not be suitable for representing the hydrological processes for this period.

#### 3.2. Water Quality Modeling

#### 3.2.1. TSS Loads

#### 3.2.2. TSS Dynamics

_{R}

_{²}are shown in Figure 6. Visual assessment of model outputs reveals an important advantage of the applied approaches: the ability to replicate multiple peaks of TSS concentrations. This was a forgone result for the homothetic model, but not for the others. Observation of the pollutographs shows that, depending on the model and the rainfall, the simulated beam does not frame the entire observations with a varying level of coverage. However, the width of the beam is narrow, revealing small uncertainties associated with simulated TSS concentrations. Accounting for the variability of pollutant generation and transport mechanisms at the elemental scale of the UHE leads to small uncertainties regarding the estimate of the TSS concentrations dynamics at the outlet. The stochastic representation of the processes thus succeeded in assessing the spatial propagation of uncertainty throughout the catchment area.

_{RMSE}all fell within the same range. However, the determination coefficients show the limitations of the model in coping with the intra-event variability of TSS concentrations, particularly for App-2 and -3. Visual observation of the pollutographs shows that the simulated dynamics with the stochastic SWMM model were in accordance with the general decreasing tendency of TSS concentrations. However, coverage of the pollutographs regarding simulations was variable. For the first event, the model failed to replicate the initial rise in the concentrations, but succeeded in replicating the second peak, as well as the small rise at the end of the event. For the other two events, the simulations replicated the highest peak occurring at the beginning of the rainfall event, but overestimated the concentrations, since the beam was higher than the measurement. Therefore, the decrease in concentrations was accurately replicated for the second event, while this was underestimated for the steady phase recorded for the third event. The pollutographs simulated with the homothetic model did not succeed in replicating the initial peaks, but were able to better cope with steady phase fluctuations, with an underestimation for the first event and an overestimation recorded for the second and third. The M(V) curve model completely failed in simulating the dynamics of TSS. The obtained pollutographs were constant during the majority of the event, with the appearance of a small peak at the end of two of the events. The most acceptable simulation is for the event of 15 November, as a small peak of TSS appears at the beginning of the pollutographs, which rapidly decreases into the constant phase.

#### 3.2.3. Spatial Variability of TSS Loads

^{2}, while it is 20 g/m

^{2}and 6 g/m

^{2}, respectively for the roads and the roofs. On the UHE scale, higher loads were derived from parcels connected to the boulevard. The loads generated by the roads mostly ranged between 1.5 and 3 g/m

^{2}, regardless of the road fraction. However, assuming that all roads are subject to the same traffic density, larger areas must have a larger contaminant yield, just as areas in closer proximity to traffic must also have a higher contamination than isolated areas [40]. As such, the distance of the cadastral parcel from the adjacent road and the fraction of the adjacent road connected to the parcel should be incorporated into the sampling of the EMC, in order to give a more explicit account of the effect of traffic on pollutant generation. The relationship between these parameters and the EMC could be represented by accounting for an exponentially decreasing function with the distance to the street.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Table A1.**Characteristics of the simulated rainfall events for the calibration period from October 2014 until January 2015. (ADWP is the antecedent dry weather period).

Duration (min) | ADWP (hours) | Rainfall Depth (mm) | Maximum Intensity (mm/h) | |
---|---|---|---|---|

Min | 52 | 0.8 | 2 | 1.1 |

Max | 720 | 274.4 | 22.1 | 42.3 |

Mean | 185.4 | 61.7 | 5.7 | 8.3 |

Median | 124 | 37.2 | 3.8 | 5.3 |

d10 | 57.6 | 1.7 | 2.3 | 1.1 |

d90 | 347 | 175.1 | 11.9 | 15.2 |

**Table A2.**Characteristics of the nine rainfall events for which water quality modeling results were exploited.

Beginning Date | End Date | Duration (min) | ADWP (hours) | Precipitation Height (mm) | Maximum Intensity (mm/h) |
---|---|---|---|---|---|

8 Oct. 2014 04:48 | 8 Oct. 2014 09:34 | 288 | 11.8 | 9.1 | 6.89 |

8 Oct. 2014 17:10 | 8 Oct. 2014 20:40 | 212 | 8 | 7.47 | 10.1 |

9 Oct. 2014 20:18 | 9 Oct. 2014 21:10 | 54 | 24 | 4.63 | 42 |

12 Oct. 2014 13:26 | 12 Oct. 2014 15:22 | 118 | 64.5 | 3.54 | 6.9 |

7 Nov. 2014 05:52 | 7 Nov. 2014 07:54 | 124 | 76.5 | 3.77 | 6.71 |

14 Nov. 2014 09:20 | 14 Nov. 2014 13:08 | 230 | 170 | 7.42 | 7.95 |

15 Nov. 2014 00:18 | 15 Nov. 2014 04:42 | 266 | 11.4 | 12.83 | 5.54 |

26 Nov. 2014 00:44 | 26 Nov. 2014 02:34 | 112 | 221 | 3.4 | 4.99 |

19 Dec. 2014 13:54 | 19 Dec. 2014 16:04 | 132 | 52.7 | 3.39 | 12.2 |

**Table A3.**Values of physical and transfer parameters for hydrological modeling of the Le Perreux catchment.

Parameter | Unit | Description | Value |
---|---|---|---|

S_{tree,min} | mm | Minimum value of the tree interception | 1 |

A | min^{−1} | Drainage law coefficient for tree interception | 0.04 |

S_{max,soil} | Mm | Maximum capacity of the surface reservoir for the natural soil | 5 |

S_{max,roof} | Mm | Maximum capacity of the surface reservoir for the roof | 0.5 |

S_{max,street} | Mm | Maximum capacity of the surface reservoir for the street | 3.5 |

K_{s,soil} | m/s | Hydraulic conductivity at natural saturation for the natural soil | 10^{−5} |

K_{s,street} | m/s | Hydraulic conductivity at natural saturation for the street | 10^{−8} |

M | - | Scaling parameter of the hydraulic conductivity | 5 |

${\theta}_{s}$ | - | Water content at natural saturation | 0.43 |

${\psi}_{e}$ | - | Suction head at air entry | 0.05 |

Z_{root} | m | Root depth | 1.5 |

Λ | - | Ground water drainage coefficient | 4 |

µ | - | Ground water drainage exponent | 4 |

α_{v} | - | Representative position of the vadose zone | 0.5 |

B | - | Retention curve exponent | 5 |

X | Routing parameter of Muskingum | 0.2 | |

${\theta}_{pipe}$ | Pipe filling rate | 2.51 |

## References

- Lee, J.H.; Bang, K.W. Characterization of urban stormwater runoff. Water Res.
**2000**, 34, 1773–1780. [Google Scholar] [CrossRef] - Kim, J.-Y.; Sansalone, J.J. Event-based size distributions of particulate matter transported during urban rainfall-runoff events. Water Res.
**2008**, 42, 2756–2768. [Google Scholar] [CrossRef] - Göbel, P.; Dierkes, C.; Coldewey, W.G. Storm water runoff concentration matrix for urban areas. J. Contam. Hydrol.
**2007**, 91, 26–42. [Google Scholar] [CrossRef] - Elliott, A.; Trowsdale, S. A review of models for low impact urban stormwater drainage. Environ. Model. Softw.
**2007**, 22, 394–405. [Google Scholar] [CrossRef] - Zoppou, C. Review of urban storm water models. Environ. Model. Softw.
**2001**, 16, 195–231. [Google Scholar] [CrossRef] - Tsihrintzis, V.A.; Hamid, R. Modeling and management of urban stormwater runoff quality: A review. Water Resour. Manag.
**1997**, 11, 136–164. [Google Scholar] [CrossRef] - Dotto, C.B.S.; Kleidorfer, M.; Deletic, A.; Rauch, W.; McCarthy, D.T.; Fletcher, T.D. Performance and sensitivity analysis of stormwater models using a Bayesian approach and long-term high resolution data. Environ. Model. Softw.
**2011**, 26, 1225–1239. [Google Scholar] [CrossRef] - Rossman, L.A. Storm Water Management Model User’s Manual, Version 5.0; National Risk Management Research Laboratory, Office of Research and Development, US Environmental Protection Agency Cincinnati: Washington, DC, USA, 2010. [Google Scholar]
- Bujon, G. Prévision des débits et des flux polluants transités par les réseaux d’égouts par temps de pluie. Le modèle FLUPOL. Houille Blanche
**1988**. [Google Scholar] [CrossRef] - Sage, J.; Bonhomme, C.; Al Ali, S.; Gromaire, M.-C. Performance assessment of a commonly used “accumulation and wash-off” model from long-term continuous road runoff turbidity measurements. Water Res.
**2015**, 78, 47–59. [Google Scholar] [CrossRef] [Green Version] - Al Ali, S.; Bonhomme, C.; Chebbo, G. Evaluation of the Performance and the Predictive Capacity of Build-up and Wash-off Models on Different Temporal Scales. Water
**2016**, 8, 312. [Google Scholar] [CrossRef] - Chen, L.; Gong, Y.; Shen, Z. Structural uncertainty in watershed phosphorus modeling: Toward a stochastic framework. J. Hydrol.
**2016**, 537, 36–44. [Google Scholar] [CrossRef] - Kanso, A.; Tassin, B.; Chebbo, G. A benchmark methodology for managing uncertainties in urban runoff quality models. Water Sci. Technol.
**2005**, 51, 163–170. [Google Scholar] [CrossRef] [PubMed] - Wijesiri, B.; Egodawatta, P.; McGree, J.; Goonetilleke, A. Understanding the uncertainty associated with particle-bound pollutant build-up and wash-off: A critical review. Water Res.
**2016**, 101, 582–596. [Google Scholar] [CrossRef] [PubMed] - Lindblom, E.; Ahlman, S.; Mikkelsen, P.S. Uncertainty-based calibration and prediction with a stormwater surface accumulation-washoff model based on coverage of sampled Zn, Cu, Pb and Cd field data. Water Res.
**2011**, 45, 3823–3835. [Google Scholar] [CrossRef] - Freni, G.; Mannina, G. Bayesian approach for uncertainty quantification in water quality modeling: The influence of prior distribution. J. Hydrol.
**2010**, 392, 31–39. [Google Scholar] [CrossRef] [Green Version] - Sage, J.; Bonhomme, C.; Emmanuel, B.; Gromaire, M.C. Assessing the Effect of Uncertainties in Pollutant Wash-Off Dynamics in Stormwater Source-Control Systems Modeling: Consequences of Using an Inappropriate Error Model. J. Environ. Eng.
**2017**, 143, 04016077. [Google Scholar] [CrossRef] - Egodawatta, P.; Thomas, E.; Goonetilleke, A. Mathematical interpretation of pollutant wash-off from urban road surfaces using simulated rainfall. Water Res.
**2007**, 41, 3025–3031. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Liu, A.; Egodawatta, P.; Guan, Y.; Goonetilleke, A. Influence of rainfall and catchment characteristics on urban stormwater quality. Sci. Total Environ.
**2013**, 444, 255–262. [Google Scholar] [CrossRef] [Green Version] - McCarthy, D.T.; Hathaway, J.M.; Hunt, W.F.; Deletic, A. Intra-event variability of Escherichia coli and total suspended solids in urban stormwater runoff. Water Res.
**2012**, 46, 6661–6670. [Google Scholar] [CrossRef] - Gromaire-Mertz, M.C.; Garnaud, S.; Gonzalez, A.; Chebbo, G. Characterisation of urban runoff pollution in Paris. Water Sci. Technol.
**1999**, 39, 1–8. [Google Scholar] [CrossRef] - Lamprea, D.K. Caractérisation et Origine des Métaux Traces, Hydrocarbures Aromatiques Polycycliques et Pesticides Transportés par les Retombées Atmosphériques et les Eaux de Ruissellement Dans les Bassins Versants Séparatifs Péri-Urbains; Ecole Centrale de Nantes (ECN): Nantes, France, 2009. [Google Scholar]
- Hong, Y.; Bonhomme, C.; Le, M.-H.; Chebbo, G. A new approach of monitoring and physically-based modeling to investigate urban wash-off process on a road catchment near Paris. Water Res.
**2016**, 102, 96–108. [Google Scholar] [CrossRef] - Deletic, A.B.; Orr, D.W. Pollution Buildup on Road Surfaces. J. Environ. Eng.
**2005**, 131, 49–59. [Google Scholar] [CrossRef] - Akan, A.O. Derived Frequency Distribution for Storm Runoff Pollution. J. Environ. Eng.
**1988**, 114, 1344–1351. [Google Scholar] [CrossRef] - Chen, J.; Adams, B.J. A derived probability distribution approach to stormwater quality modeling. Adv. Water Resour.
**2007**, 30, 80–100. [Google Scholar] [CrossRef] - Daly, E.; Bach, P.M.; Deletic, A. Stormwater pollutant runoff: A stochastic approach. Adv. Water Resour.
**2014**, 74, 148–155. [Google Scholar] [CrossRef] - Wong, T.H.; Fletcher, T.D.; Duncan, H.P.; Coleman, J.R.; Jenkins, G.A. A Model for Urban Stormwater Improvement: Conceptualization. In Proceedings of the 9th International Conference on Urban Drainage, Portland, OR, USA, 8–13 September 2002; pp. 1–14. [Google Scholar]
- Rodriguez, F.; Andrieu, H.; Morena, F. A distributed hydrological model for urbanized areas—Model development and application to case studies. J. Hydrol.
**2008**, 351, 268–287. [Google Scholar] [CrossRef] - Bárdossy, A. Calibration of hydrological model parameters for ungauged catchments. Hydrol. Earth Syst. Sci. Discuss.
**2007**, 11, 703–710. [Google Scholar] [CrossRef] [Green Version] - Refsgaard, J.C. Parameterisation, calibration and validation of distributed hydrological models. J. Hydrol.
**1997**, 198, 69–97. [Google Scholar] [CrossRef] - Bertrand-Krajewski, J.-L.; Chebbo, G.; Saget, A. Distribution of pollutant mass vs volume in stormwater discharges and the first flush phenomenon. Water Res.
**1998**, 32, 2341–2356. [Google Scholar] [CrossRef] - Bonhomme, C.; Petrucci, G. Spatial Representation in Semi-Distributed Modeling of Water Quantity and Quality. Presented at International Conference on Urban Drainage, Kuching, Malaysia, 7–12 September 2014; p. 2488399. [Google Scholar]
- Green, I.R.A.; Stephenson, D. Criteria for comparison of single event models. Hydrol. Sci. J.
**1986**, 31, 395–411. [Google Scholar] [CrossRef] [Green Version] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Al Ali, S.; Bonhomme, C.; Dubois, P.; Chebbo, G. Investigation of the wash-off process using an innovative portable rainfall simulator allowing continuous monitoring of flow and turbidity at the urban surface outlet. Sci. Total Environ.
**2017**, 609, 17–26. [Google Scholar] [CrossRef] [PubMed] - Baladès, J.D.; Petitnicolas, F. Les strategies de reduction des flux pollutants par temps de pluie a la source: Approche technico-economique. Novatech
**2001**, 1, 367–373. [Google Scholar] - Van Buren, M.A.; Watt, W.E.; Marsalek, J. Application of the log-normal and normal distributions to stormwater quality parameters. Water Res.
**1997**, 31, 95–104. [Google Scholar] [CrossRef] - Charbeneau, R.J.; Barrett, M.E. Evaluation of methods for estimating stormwater pollutant loads. Water Environ. Res.
**1998**, 70, 1295–1302. [Google Scholar] [CrossRef] - Saeedi, M.; Hosseinzadeh, M.; Jamshidi, A.; Pajooheshfar, S.P. Assessment of heavy metals contamination and leaching characteristics in highway side soils, Iran. Environ. Monit. Assess.
**2009**, 151, 231–241. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Illustration of detailed spatial representation of an urban catchment in Nantes, France within the Urban Runoff Branching Structure (URBS) model, showing the characteristic cadastral size (adapted from [29]). In the figure, an urban hydrological element (UHE) is delineated by a dashed bold line, which encompasses a cadastral parcel and its adjacent street surface. The connection point to the hydrological network is represented as (Pc).

**Figure 2.**Cadastral parcels of the Le Perreux catchment. White parcels represent the UHEs, including a fraction of the adjacent street. Red dashed parcels represent isolated UHEs. The blue lines and the red circle represent the segments of the hydrological network and the catchment outlet respectively.

**Figure 3.**The studied catchment and the runoff branching network (including both street and sewer segments). The red point represents the outlet of the catchment.

**Figure 4.**Water flow simulations for four events from the period from 8 October 2014 to 31 December 2014. The simulated flow at the outlet is represented by red circles. The measured flow is represented by grey squares. The rainfall intensity is plotted on the upper part of the figures.

**Figure 5.**Boxplots of simulated wash-off load obtained with the three modeling approaches. The central red mark is the median, the edges are the 25th and the 75th percentiles and the whiskers extend to the extreme values that are not considered as outliers. The measured wash-off load is presented as blue circles.

**Figure 6.**Best performance events based on TSS concentrations using C

_{R}

_{²}and the C

_{RMSE}criteria for two rainfall events on 8 October, and one on 15 November simulated with (

**a**) App-1: SWMM, (

**b**) App-2: Homothety and (

**c**) App-3: M(V) curve. The rainfall intensity is plotted on the upper part of the graphs. The solid blue lines represent the measured TSS concentrations. The rainbow-colored lines marked with circles represent the simulated TSS concentrations, where each color represents the TSS concentrations for one simulation.

**Figure 7.**Spatial variability of mean TSS washed-off loads (g/m

^{2}) from the (

**a**) UHE, (

**b**) roads and alleys and (

**c**) roofs for the rainfall event of 15th November.

**Table 1.**Summary of total suspended solids (TSS) modeling approaches and the corresponding parameters.

Stormwater Quality Approach | Water Quality Model | Φ | Land Use | Ω |
---|---|---|---|---|

First approach (App-1) | Exponential SWMM | EMC (mg/L) | Roof | [13–60] |

Road | [82–200] | |||

C_{1} | Roof/Road | [0.01–1.5] | ||

C_{2} | [0.8–1.9] | |||

Second approach (App-2) | Homothetic hydrograph | EMC (mg/L) | Roof | [13–60] |

Road | [82–200] | |||

Third approach (App-3) | M(V) curve | EMC (mg/L) | Roof | [13–60] |

Road | [82–200] | |||

B | Roof/Road | [0.5–1.2] |

**Table 2.**Evaluation criteria of the performance of hydrological and water quality models. $Si{m}_{t}$ is the simulated value at time t; $Ob{s}_{t}$ is the observed value at time t; $\overline{Sim}$ is the average of the simulated values; $\overline{Obs}$ is the average of the observed values; ${t}_{1}$ is the beginning of the simulated event; ${t}_{n}$ is the end of the simulated event; n is the total duration of the simulated event.

Statistical Criterion | Equation | Applied for the Evaluation of | |
---|---|---|---|

Hydrological Model | Water Quality Model | ||

Nash Sutcliffe coefficient (${C}_{Nash}$) | ${C}_{Nash}=1-\frac{{{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}{\left(Si{m}_{t}-Ob{s}_{t}\right)}^{2}}{{{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}{\left(Ob{s}_{t}-\overline{Obs}\right)}^{2}}$ | √ | _ |

Determination coefficient (${C}_{R\xb2}$) | ${C}_{R\xb2}=\frac{\left({{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}\left(Si{m}_{t}-\overline{Sim}\right)(Ob{s}_{t}-\overline{Obs}\right){)}^{2}}{{{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}\left(Si{m}_{t}-\overline{Sim}\right)\xb2{{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}\left(Ob{s}_{t}-\overline{Obs}\right)\xb2}$ | √ | √ |

Root mean square error (C_{RMSE}) | ${C}_{RMSE}=\sqrt{\frac{{{\displaystyle \sum}}_{{t}_{1}}^{{t}_{n}}\left(Si{m}_{t}-Ob{s}_{t}\right)\xb2}{n}}$ | _ | √ |

**Table 3.**Evaluation criteria for simulations of event runoff volumes (V) and instantaneous flow (Q) for the calibration (n = 30 events) and validation (n = 4 events) periods.

C_{R}_{²} | C_{Nash} | |
---|---|---|

Calibration (8 Oct. 2014/Jan. first 2015; n = 30) | ||

V | 0.93 | 0.9 |

Q | 0.77 | 0.71 |

Validation (31 Mar. 2015/27 Apr. 2015; n = 4) | ||

V | 0.99 | 0.56 |

Q | 0.91 | 0.58 |

**Table 4.**Mean [Min Max] Determination and RMSE coefficients calculated between the observed and simulated TSS concentrations for three modeling approaches for each of the nine events. The grey cells represent the simulations for which the C

_{R}

_{²}is higher than 0.5.

C_{R}_{²} | C_{RMSE} | |||||
---|---|---|---|---|---|---|

App-1 | App-2 | App-3 | App-1 | App-2 | App-3 | |

8 Oct. 2014 04:48 | 0.22[0.18 0.3] | 0.01[0.002 0.018] | 0.47[0.41 0.55] | 46[37–42] | 41[39 42] | 42[41 43] |

8 Oct. 2014 17:10 | 0.8[0.73 0.77] | 0.59[0.57 0.6] | 0.2[0.11 0.32] | 34[28 30] | 33[31 35] | 37[34 39] |

9 Oct. 2014 20:18 | 0.1[4.53 × 10 ^{−3} 0.45] | 0.17[0.12 0.21] | 0.06[0.003 0.14] | 86[39 321] | 45[44 46] | 43[42 45] |

12 Oct. 2014 13:26 | 0.1[0.06 0.16] | 0.52[0.49 0.54] | 0.02[8.2 × 10 ^{−5} 0.08] | 235[234 236] | 232[231 234] | 236[234 238] |

7 Nov. 2014 05:52 | 0.24[0.22 0.26] | 0.06[0.05 0.07] | 0.18[0.15 0.2] | 57[56 59] | 47[46 50] | 47[44 48] |

14 Nov. 2014 09:20 | 0.003[0.11 0.013] | 0.07[0.06 0.09] | 0.13[0.1 0.17] | 69[68 72] | 76[75 77] | 63[61 65] |

15 Nov. 2014 00:18 | 0.84[0.83 0.85] | 0.09[0.08 0.1] | 0.5[0.43 0.62] | 99[89 108] | 45[43 47] | 36[34 38] |

26 Nov. 2014 00:44 | 0.04[0.03 0.07] | 0.33[0.29 0.39] | 9.4 × 10^{−4}[8.8 × 10 ^{−6} 0.003] | 92[90 93] | 84[83 86] | 92[91 93] |

19 Dec. 2014 13:54 | 0.03[0.0012 0.005] | 0.003[0.0012 0.0047] | 0.017[0.011 0.022] | 816.8[816.4 817] | 821[820 822] | 818.9[818.8 819.1] |

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## Share and Cite

**MDPI and ACS Style**

Al Ali, S.; Rodriguez, F.; Bonhomme, C.; Chebbo, G.
Accounting for the Spatio-Temporal Variability of Pollutant Processes in Stormwater TSS Modeling Based on Stochastic Approaches. *Water* **2018**, *10*, 1773.
https://doi.org/10.3390/w10121773

**AMA Style**

Al Ali S, Rodriguez F, Bonhomme C, Chebbo G.
Accounting for the Spatio-Temporal Variability of Pollutant Processes in Stormwater TSS Modeling Based on Stochastic Approaches. *Water*. 2018; 10(12):1773.
https://doi.org/10.3390/w10121773

**Chicago/Turabian Style**

Al Ali, Saja, Fabrice Rodriguez, Céline Bonhomme, and Ghassan Chebbo.
2018. "Accounting for the Spatio-Temporal Variability of Pollutant Processes in Stormwater TSS Modeling Based on Stochastic Approaches" *Water* 10, no. 12: 1773.
https://doi.org/10.3390/w10121773